Consider the Following Probability Transition Matrix Find the Classes of This Markov Chain and Determine Whether

Short Answer

Consider the following probability transition matrix: $$\left( \begin{array} { c c c c c c } 0 & 1 & 0 & 0 & 0 & 0 \\.4 & .6 & 0 & 0 & 0 & 0 \\.3 & 0 & .4 & .2 & .1 & 0 \\0 & 0 & 0 & .3 & .7 & 0 \\0 & 0 & 0 & .5 & 0 & .5 \\0 & 0 & 0 & .3 & 0 & .7\end{array} \right)$$ Find the classes of this Markov chain and determine whether each is recurrent or transient.